Algebra 2 Problem

[mustang]

Problem 43.
Solve and check.
7^3x divided by 2^7x-1 = (43.2)^x+2

[HallsofIvy]

I am assuming this is that you meant
\frac{7^{3x}}{2^{7x-1}}= 43.2^{x+2}
rather than
\frac{7^3x}{2^7x-1}= 43.2^x+ 2
which would be harder.

The key step is to use the logarithm to get rid of the "exponentials" (It really doesn't matter which base logarithm you use):
log(\frac{7^{3x}}{2^{7x-1}})= log(43.2^{x+2})
which is:
log(7^{3x})- log(2^{7x-1})= log(34.2^{x+2})
[tex] 3x log(7)- (7x-1)log(2)= (x+2)log(34.2)

That's now a simple linear equation with some peculiar coefficients.